A Partial Reciprocal of Dirichlet Lagrange Theorem Detected by Jets

• Manuel Valentim de Pera Garcia ^[1] ; Gerard John Alva Morales ^[1]
  1. [1] Universidade de São Paulo

     Universidade de São Paulo

     Brasil

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 2, 2017, págs. 371-389
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study the stability of an equilibrium point in a conservative Hamiltonian system in the case that equilibrium is not a minimum of the potential energy and this fact is shown by a jet of this function. Thanks to a modification of a result of Krasovskii, we prove that for a large class of systems under these conditions equilibrium is unstable and there is an asymptotic trajectory to that point.